35=2(x-5)^2 eching

$$35 = 2 ( x - 5 ) ^ { 2 }$$

x uchun yechish

$$x=\frac{\sqrt{70}}{2}+5\approx 9,183300133$$

$$x=-\frac{\sqrt{70}}{2}+5\approx 0,816699867$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikki tarafini 2 ga bo‘ling.

$$\frac{35}{2}=\left(x-5\right)^{2}$$

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(x-5\right)^{2} kengaytirilishi uchun ishlating.

$$\frac{35}{2}=x^{2}-10x+25$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$x^{2}-10x+25=\frac{35}{2}$$

Ikkala tarafdan \frac{35}{2} ni ayirish.

$$x^{2}-10x+25-\frac{35}{2}=0$$

\frac{15}{2} olish uchun 25 dan \frac{35}{2} ni ayirish.

$$x^{2}-10x+\frac{15}{2}=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -10 ni b va \frac{15}{2} ni c bilan almashtiring.

$$x=\frac{-\left(-10\right)±\sqrt{\left(-10\right)^{2}-4\times \frac{15}{2}}}{2}$$

-10 kvadratini chiqarish.

$$x=\frac{-\left(-10\right)±\sqrt{100-4\times \frac{15}{2}}}{2}$$

-4 ni \frac{15}{2} marotabaga ko'paytirish.

$$x=\frac{-\left(-10\right)±\sqrt{100-30}}{2}$$

100 ni -30 ga qo'shish.

$$x=\frac{-\left(-10\right)±\sqrt{70}}{2}$$

-10 ning teskarisi 10 ga teng.

$$x=\frac{10±\sqrt{70}}{2}$$

x=\frac{10±\sqrt{70}}{2} tenglamasini yeching, bunda ± musbat. 10 ni \sqrt{70} ga qo'shish.

$$x=\frac{\sqrt{70}+10}{2}$$

10+\sqrt{70} ni 2 ga bo'lish.

$$x=\frac{\sqrt{70}}{2}+5$$

x=\frac{10±\sqrt{70}}{2} tenglamasini yeching, bunda ± manfiy. 10 dan \sqrt{70} ni ayirish.

$$x=\frac{10-\sqrt{70}}{2}$$

10-\sqrt{70} ni 2 ga bo'lish.

$$x=-\frac{\sqrt{70}}{2}+5$$

Tenglama yechildi.

$$x=\frac{\sqrt{70}}{2}+5 x=-\frac{\sqrt{70}}{2}+5$$

Kvadratni yakunlash bo'yicha qadamlar

Ikki tarafini 2 ga bo‘ling.

$$\frac{35}{2}=\left(x-5\right)^{2}$$

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(x-5\right)^{2} kengaytirilishi uchun ishlating.

$$\frac{35}{2}=x^{2}-10x+25$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$x^{2}-10x+25=\frac{35}{2}$$

x^{2}-10x+25 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-5\right)^{2}=\frac{35}{2}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-5\right)^{2}}=\sqrt{\frac{35}{2}}$$

Qisqartirish.

$$x-5=\frac{\sqrt{70}}{2} x-5=-\frac{\sqrt{70}}{2}$$

5 ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{70}}{2}+5 x=-\frac{\sqrt{70}}{2}+5$$